ATLANTA — Republicans are on the verge of winning a majority so large in Georgia’s Legislature that they could offer changes to the state constitution without Democratic support. Whether they can effectively use that power is another question.

Winning a two-thirds majority, often called a supermajority, in the House and Senate would prove a Republican accomplishment. It was only a decade ago that Sonny Perdue became the first Republican to become governor since Reconstruction following the Civil War. Republican control of the state Senate came that same year, followed by the House of Representatives two years later.

In theory, having a two-thirds majority would allow Republicans to offer amendments to the state constitution without modifying their stances to attract Democratic lawmakers and overturn vetoes from the Republican governor. Any constitutional amendments would still be subject to voter approval. When counting Republicans who are unopposed and assuming the party’s incumbents win, the GOP will hold 112 seats in the House next year, meaning they would need eight more seats for a supermajority. Judging by the same standard, the GOP is three seats shy in the Senate.

Because Republicans controlled the recent redistricting process, their candidates in open districts are more likely to face friendly voters than Democrats.

“What you have to be mindful of is that as we grow as a party and as our numbers grow, we’re a diverse party,” said House Speaker David Ralston (R-Blue Ridge). “The larger the number, you know, sometimes it gets to be a little more problematic keeping everyone herded together and voting the same way. I don’t think there’s automatic slam dunks.”

Although they form a minority, Democratic leaders say their presence has a moderating effect on Republicans. To change the constitution, the GOP is forced to work with Democrats, which involves give-and-take.

“The more they get toward actually having a supermajority, the less compromise to the middle they’ll have to make within their own party and trying to get Democratic votes,” said Sen. Steve Henson of Tucker, the Democratic leader in the Senate. “It will make a difference.”

The recent debate over charter schools in Georgia illustrates that having a large majority does not necessarily mean having the votes for sweeping changes. Last year, the state Supreme Court ruled that a commission created by lawmakers in 2008 was unconstitutional because it gave tax dollars to charter schools over the objection of local school boards.

In response, Republicans pushed to change Georgia’s constitution so state officials could authorize new charter schools. Despite intense lobbying by top-ranking Republicans, several GOP lawmakers voted against the amendment. Rural Republicans, for example, feared it would take money from rural districts to spend on charter schools in urban areas. Other Republicans allied with the tea party movement criticized the bill as an attack on local control.

Enough lawmakers backed the resolution in the end, allowing it to pass the House and ultimately the Senate. Voters will decide next month whether to allow the change to the state constitution.

Former Senate President Pro Tem Eric Johnson, a Republican, said Democrats in Georgia originally suffered from competing interests within their own party, such as urban Democrats who clashed with conservative rural Democrats.

“Now it’s slipped,” he said. “Now the Democratic party is isolated to urban liberal ideology, and the Republicans have the bigger tent going from rural conservatives to suburban moderates to libertarian. So if it’s a more complex issue, then it’s going be hard. Just because they have two-thirds doesn’t mean they’re going to agree.”

If the GOP wins a supermajority, the interest groups that helped them gain seats will come asking for votes. For example, Georgia Right To Life wants the state to adopt a so-called personhood amendment, which would effectively ban abortion except for pregnancies that threaten a mother’s life. Dan Becker, the organization’s president, said he is not sure Republicans will win a supermajority but is ready to move when they do.

The proposed amendment has been introduced before but never advanced.

“As soon as we have a supermajority, that’s exactly what we’re going to press for,” Becker said.

Ralston was noncommittal on whether he would support such an amendment, saying he had not even read it. He noted that Georgia lawmakers passed fresh restrictions on abortion last year and that the personhood amendment has failed elsewhere.

“I’m aware that in a conservative state like Mississippi it was not successful at the polls,” he said.

Democrats, if they do find themselves on the opposite side of a supermajority, will have to work to build coalitions. Rep. Stacey Abrams, the Democratic minority leader, said Republicans may find it difficult to turn away special interest groups seeking help from a GOP supermajority they worked to create.

“How many times can you say ‘no’ before something has to move forward?” she said.

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